Recently, I watched the American film “Oppenheimer,” which depicts the life of the genius physicist, Oppenheimer, known as the father of atomic bombs.

Note: Although, it's not grammatically incorrect, in more formal texts we would write the full names of people out.
Example: ". . . which depicts the life of the genius physicist, J. Robert Oppenheimer. . ."

Despite its acclaim, I was hesitant to watch it as a Japanese person, as the atomic bombs he created devastated Hiroshima and Nagasaki in 1945.

After successfully detonating bombs in the war against Japan, Oppenheimer said, “I’veNow I am become Death, I am now the destructooyer of worlds.” This suggests he may have repented of creating such a terrible bomb.

Not a grammatical error, but changed the quote to be verbatim what was said in English originally.

All world leaders should heed these words and prevent the use and even production of nuclear weapons.

Alternately: All world leaders should heed these words and prevent the proliferation of nuclear weapons.

Proliferation is defined as the spread of nuclear weapons, their technology, and fissile materials.

The Japanese government must more strongly appeal for the abolishment of nuclear abolitiweapons.

Or: The Japanese government must more strongly advocate for nuclear disarmament.

Recently, I watched the American film “Oppenheimer,” which depicts the life of the genius physicist, Oppenheimer, known as the father of the atomic bombs.

Though it's technically correct that he is "the father of atomic bombs," the saying is "the father of the atomic bomb." The meaning of this saying is not so much that he is the father of 1 atomic bomb, nor even "the first atomic bomb," but that he is the father of "the concept" of atomic bombs (which you can absolutely argue is factually wrong, but that's how the saying goes).
This kind of wording where "<someone> is the father/founder of <something>" and <something> is made singular whilst still broadly applying to <something>, is really common in English.

After successfully detonating the bombs in the war against Japan, Oppenheimer said, “I’veNow I am become Death, I am now the destructooyer of worlds.” This suggests he may have repented ofor creating such a terrible bombweapon.

"successfully detonating bombs," is correct English, but since since it wasn't just "any random bombs," but rather, "the nuclear bombs" that were established earlier in this paragraph, using "the bombs" gives the subtle meaning that we are referring to "THE nuclear bombs."

"bomb" is correct, but sounds slightly repetitive to the first "bombs" in the sentence. An other synonym in this context could be "device."

All world leaders should heed these words and prevent the use and even production of nuclear weapons.

I whole heartedly agree with this sentiment. I wish that everyone would dismantle every single nuke on the planet, for the sake of humanity!

Japan is the only country to have experienced nuclear disasteratrocities.

Your sentence is grammatically correct, but technically other places have experienced nuclear disasters (Chornobyl for example) as a "disaster" can be accidental, but an "atrocity" is intentional.

Recently, I watched the American film “Oppenheimer,” which depicts the life of the genius physicist, J. Robert Oppenheimer, known as the father of atomic bombs.

It's a little bit strange to refer to people by only their last names. When talking about a famous historical figure, we'd usually try to use their full name. But otherwise, you could also say "...of the genius physicist of the same name..." For instance, if you don't actually know their full name.

Side note: you could also potentially leave out the name and use "eponymous" here: "...which depicts the life of the eponymous genius physicist, known as..." However, it is a very formal word that not even a lot of native speakers understand. It means: "with the same name as what I have mentioned before." If I say "John Smith and his eponymous book", that means that book is, itself, named "John Smith."

After successfully detonating bombs in the war against Japan, Oppenheimer said, “I’ve become Death, I am now the destructor of worlds.” This suggests he may have repented ofgretted creating such a terrible bomb.

"Repent" has a very dramatic connotation and implies that there is a very special action to accompany the thought, like a ritual. "Regret" would work better in this situation.

Japan is the only country to have experienced nuclear disasters.

Perfectly fine on its own, but this feels just a little more natural to me for some reason.

The Japanese government must more strongly appeal for nuclear abolition more.

This works, but "more strongly" feels like an odd pairing of words to me for some reason, so I've moved "more" to the end. Also, you can also say "support" instead of "appeal for".

However, somehow, I cannot help but feel pessimistic about this issueall of this.

I personally like to say "all of this" or "all this" when I'm talking about any sort of situation that's on my mind, especially for a current event.

Recently, I watched the American film “Oppenheimer,” which depicts the life of the genius physicist, Oppenheimer, known as the father of atomic bombs.

You should include his full name, it just sounds strange no offense

Despite its acclaim, I was hesitant to watch it as a Japanese person, as the atomic bomb he created devastated Hiroshima and Nagasaki in 1945.

LOL

However, I believe this film is worth seeing now, as a war-loving dictator threatens to use nuclear weapons.

However, my view has changed and I believe this film is worth seeing now, as a war-loving dictator threatens to use nuclear weapons.

The Japanese government must more strongly appeal for nuclear abolition.

The Japanese government should support nuclear abolition.